Change in momentum and change in Kinetic energy

In summary, the conversation discusses the changes in momentum and kinetic energy of a particle that is thrown vertically upwards with initial speed v and returns to its starting point. The equations P=mv and KE=1/2mv2 are mentioned, and it is suggested to use the equations of motion and kinematics to calculate the velocity, height, and time for the particle. By using v(t) = v - gt and t = v/g, the height and time can be calculated, and then the velocity at the starting point can be determined to prove the change in momentum to be 2mv and no change in kinetic energy.
  • #1
eureka_beyond
20
0

Homework Statement


A particle of mass m is thrown vertically upwards with initial speed v. When the particle returns to it starting point, what are the changes in momentum and kinetic energy of the particle.


Homework Equations


P=mv KE=1/2mv2

The Attempt at a Solution


The answer to this question is change in momentum = 2mv while there's no change in KE, but I really don't understand how to calculate them?
 
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  • #2
Any ideas? Start by writing down the equations of motion for a vertical throw. Can you find the velocity at the when the body reaches its starting point again?
 
  • #3
Should I apply v2-u2=2as ? Then I'll know how high does the particle reach, which is v2/20, but how will that help me with the question? Or am I using the wrong equation?
 
  • #4
First calculate the height the particle reaches (measured from the starting reference point). Then, calculate the time it takes for the particle to fall down along that "height". Then you can calculate the velocity of the particle at the starting point (i.e. momentum and kinetic energy).
 
  • #5
using 2as=v2-u2, I know s=(v2)/20. using s=1/2at2, t=v/10...using v=u+at, I got v=v?? I don't get it...
 
  • #6
The velocity of the particle is v(t) = v - gt, when the particle is moving upwards. At the peak, v(t) = 0, and hence t = v/g. Now you can calculate the height the particle reaches. And then the time it takes to fall down again. And then the velocity at that time, and hence prove your point.
 

1. What is the difference between change in momentum and change in kinetic energy?

Change in momentum refers to the change in an object's velocity over a period of time, while change in kinetic energy refers to the change in an object's energy due to its motion. Momentum is a vector quantity, while kinetic energy is a scalar quantity. Additionally, change in momentum is directly proportional to the force applied to an object, while change in kinetic energy is directly proportional to the work done on an object.

2. How are change in momentum and change in kinetic energy related?

Change in momentum and change in kinetic energy are related through the impulse-momentum theorem. This theorem states that the change in momentum of an object is equal to the impulse applied to the object, which is the force applied over a period of time. This impulse is also equivalent to the change in kinetic energy of the object.

3. Can change in momentum be negative?

Yes, change in momentum can be negative. This indicates a decrease in an object's velocity, and therefore a decrease in its momentum. This can happen when a force is applied in the opposite direction of an object's motion, causing it to slow down.

4. What factors affect the change in kinetic energy of an object?

The change in kinetic energy of an object is affected by the mass and velocity of the object. As the mass or velocity of an object increases, its change in kinetic energy also increases. Additionally, the work done on an object by a force also affects its change in kinetic energy.

5. How is change in momentum and change in kinetic energy used in real-world applications?

The concepts of change in momentum and change in kinetic energy are used in various real-world applications, such as in car safety systems, sports equipment design, and rocket propulsion. These concepts are also important in understanding collisions and the conservation of energy in different systems.

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